Question

practice
three circular water towers are positioned side by side on a strip of land. what area is closest to the area of the shaded region? use 3.14 for π.
a. 192 in²
b. 41 in²
c. 64 in²
d. 411 in²
(image of a rectangle with three circles inside, length labeled 24 inches)

Explanation:

Step1: Find the diameter of each circle

The total length of the rectangle is 24 inches, and there are 3 circles side by side. So the diameter \( d \) of each circle is \( \frac{24}{3}=8 \) inches. Thus, the radius \( r \) of each circle is \( \frac{8}{2}=4 \) inches, and the height of the rectangle (which is equal to the diameter of the circle) is 8 inches.

Step2: Calculate the area of the rectangle

The area of a rectangle is \( A_{rectangle}=length\times width \). Here, length = 24 inches and width = 8 inches. So \( A_{rectangle}=24\times8 = 192 \) square inches.

Step3: Calculate the total area of the three circles

The area of one circle is \( A_{circle}=\pi r^{2} \). With \( \pi = 3.14 \) and \( r = 4 \), the area of one circle is \( 3.14\times4^{2}=3.14\times16 = 50.24 \) square inches. For three circles, the total area is \( 3\times50.24 = 150.72 \) square inches.

Step4: Calculate the area of the shaded region

The shaded area is the area of the rectangle minus the total area of the three circles. So \( A_{shaded}=A_{rectangle}-A_{three\ circles}=192 - 150.72 = 41.28 \) square inches, which is closest to 41 \( \text{in}^2 \).

Answer:

B. \( 41\ \text{in}^2 \)